We proposed and analyzed implementation of the single-qutrit quantum gates based on stimulated Raman adiabatic passage (STIRAP) between magnetic sublevels in atoms coupled by pulsed laser fields. This technique requires only the control of the relative phase of the driving fields but do not involve any dynamical or geometrical phases, which make it independent of the other interaction details: detuning and pulse shapes, areas and durations. The suggested techniques are immune to spontaneous emission since the qubit and qutrit manipulation proceeds through non-absorbing dark states. In this paper, taking proper timing of the Rabi frequencies allows us to transfer the population of the system to a desired superposition of the ground states with the highest fidelity. We also obtained and implemented single-qutrit unitary gates, for transferring of the population of the system with different initial and final states.